But I do have to manipulate the projection matrix... (doing AR). I therefore switched the View with view.setCompatibilityModeEnable(true);

Everything works out nicely except for the background which now appears as a canvas-filling object in the very background of the scene. To make that clearer: I now look at the cylinder from the outside.

Moving and rotating in the world still work as expected, but not for the background. It does not translate (as expected) and rotates as if it were placed around the origin (as expected), but only with the effect that it appears from the outside.